[seqfan] Re: Is A070319 the same as A068509?

[Max Alekseyev]

William,
Could please extend b-files for both sequences (say, to a thousand
terms) so that they clearly indicate differences?
Regards,
Max

On Tue, Sep 11, 2012 at 7:55 PM, William Rex Marshall
<w.r.marshall at actrix.co.nz> wrote:
> On 11/09/2012 5:25 p.m., Max Alekseyev wrote:
>>
>> It is clear that A070319(n)<= A068509(n).
>> But they are different even asymptotically: A068509(n) = O(sqrt(n))
>> while A070319(n) does not have polynomial growth.
>> I did not check what is smallest n for which they are different but
>> n=625 gives a counterexample:
>
>
> The two sequences first differ when n = 336, due to the set of 21 elements
> {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 21, 24, 30, 36, 42, 48}
> where each pair of elements has lcm <= 336, while no positive integer <= 336
> has more than 20 divisors. Therefore A068509(336) = 21 and A070319(336) =
> 20.
>
>
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